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Fwd: Fwd: Modern Techniques of Very Large Scale Optimization, Edinburgh, 19th - 20th May 2022
by Fabio Durastante 12 May '22

12 May '22

FYI -------- Messaggio Inoltrato -------- Oggetto: Fwd: Modern Techniques of Very Large Scale Optimization, Edinburgh, 19th - 20th May 2022 Data: Thu, 12 May 2022 17:14:04 +0100 Mittente: Stefano Cipolla <scipolla(a)ed.ac.uk> A: fabio.durastante(a)unipi.it ======================== Dear Colleagues, we are delighted to inform you that the workshop "Modern Techniques of Very Large Scale Optimization" will be held in Edinburgh, 19th - 20th May 2022; please see https://www.maths.ed.ac.uk/~gondzio/admm2020/home.html for more information. Although the capacity of in-person attendance is already reached we are happy for online participants to follow the talks. If you are interested and would like to attend the workshop online, then please register (free of charge) at your earliest convenience but not later than Friday 13th May. We will send you a Zoom link. Very Best regards, Jacek, Stefano, Filippo ======================== -- Stefano Cipolla Postdoctoral Research Associate School of Mathematics University of Edinburgh James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh, EH9 3FD email: scipolla(a)ed.ac.uk The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. Is e buidheann carthannais a th’ ann an Oilthigh Dhùn Èideann, clàraichte an Alba, àireamh clàraidh SC005336.

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Fwd: CENTRO DE GIORGI -- ANNOUNCEMENT -- COLLOQUIO DE GIORGI (24 May 2022)
by Fabio Durastante 12 May '22

12 May '22

*********************************************************************************** CENTRO DI RICERCA MATEMATICA "ENNIO DE GIORGI" ********************************************************************************** COLLOQUIO DE GIORGI Centro De Giorgi, Pisa, 24 May 2022 Aula Dini: 3.00 pm The event will take place in person. Andrew Wathen University of Oxford Title:“Numerical solutions methods for problems of PDE-constrained optimisation” Abstract:Since the advent of computers there has been interest in numerical methods for solving partial differential equations (PDE) problems---both methods of approximation and numerical linear algebra for the resulting sets of equations which are usually of very large dimension. Sometimes it is the solutions themselves that are of interest, but there is a significant class of problems where there is a design optimization criterion with physical constraints that are expressed in terms of PDEs; it is always the motion of fluids described by flow equations which provide the principal constraints when an engineer designs an aerodynamic structure with minimal drag and acceptable lift for example. In this talk I will consider numerical methods for such optimization problems with PDE constraints, in particular methods of iterative numerical linear algebra that render feasible the solution of such problems on advanced computers. Web site:http://www.crm.sns.it/course/6307/ <http://www.crm.sns.it/course/6307/> Please note that for organizational purposes, registration <http://www.crm.sns.it/event/493/registration.html>is mandatory. CRM Secretariat STG Puteano Centro di Ricerca Matematica "Ennio De Giorgi" Scuola Normale Superiore Piazza dei Cavalieri, 3 56126 Pisa, Italy

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Seminario di oggi (link)
by Leonardo Robol 05 May '22

05 May '22

Cari tutti/e, Il seminario di oggi sarà disponibile, oltre che in presenza, anche in streaming al solito link https://meetings.dm.unipi.it/b/leo-xik-xu4. A dopo, -- Leonardo Robol

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[Indico] Stefano Massei, Improved parallel-in-time integration via low-rank updates and interpolation, 05/05/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 04 May '22

04 May '22

Title: Improved parallel-in-time integration via low-rank updates and interpolation, Speaker(s): Stefano Massei, Università di Pisa, Date and time: 5 May 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/89 Abstract -------- This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of parallel-in-time integration leading to a class of algorithms called ParaDiag. We develop and analyze two novel approaches for the numerical solution of such equations. Our first approach is based on the observation that the modification of these equations performed by ParaDiag in order to solve them in parallel has low rank. Building upon previous work on low-rank updates of matrix equations, this allows us to make use of tensorized Krylov subspace methods to account for the modification. Our second approach is based on interpolating the solution of the matrix equation from the solutions of several modifications. Both approaches avoid the use of iterative refinement needed by ParaDiag and related space-time approaches in order to attain good accuracy. In turn, our new approaches have the potential to outperform, sometimes significantly, existing approaches. This potential is demonstrated for several different types of PDEs. -- Indico :: Email Notifier https://events.dm.unipi.it/e/89

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[Indico] Stefano Massei, Improved parallel-in-time integration via low-rank updates and interpolation, 05/05/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 27 Apr '22

27 Apr '22

Title: Improved parallel-in-time integration via low-rank updates and interpolation, Speaker(s): Stefano Massei, Università di Pisa, Date and time: 5 May 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/89 Abstract -------- This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of parallel-in-time integration leading to a class of algorithms called ParaDiag. We develop and analyze two novel approaches for the numerical solution of such equations. Our first approach is based on the observation that the modification of these equations performed by ParaDiag in order to solve them in parallel has low rank. Building upon previous work on low-rank updates of matrix equations, this allows us to make use of tensorized Krylov subspace methods to account for the modification. Our second approach is based on interpolating the solution of the matrix equation from the solutions of several modifications. Both approaches avoid the use of iterative refinement needed by ParaDiag and related space-time approaches in order to attain good accuracy. In turn, our new approaches have the potential to outperform, sometimes significantly, existing approaches. This potential is demonstrated for several different types of PDEs. -- Indico :: Email Notifier https://events.dm.unipi.it/e/89

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Ph.D. Course: An introduction to fractional calculus: fundamental ideas and numerics
by Fabio Durastante 27 Apr '22

27 Apr '22

Dear all, Monday 2 May we begin with the Ph.D. course "An introduction to fractional calculus: fundamental ideas and numerics" from 2.00 pm to 4.00 pm in the Aula Seminari. Find the latest information at: https://fdurastante.github.io/courses/introfracalculus.html#about The plan is to schedule the other lessons with those present that day. If there are people that wish to attend, but have difficulties being in person, please let me know at fabio.durastante(a)unipi.it and I'll try activating a streaming of the lecture. For any other question, feel free to write an E-mail. Best, Fabio Durastante

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[Indico] Raf Vandebril,
by leonardo.robol＠unipi.it 12 Apr '22

12 Apr '22

Title: Construction of a sequence of orthogonal rational functions, Speaker(s): Raf Vandebril, Department of Computer Science, KU Leuven, Date and time: 13 Apr 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/86 Abstract -------- Orthogonal polynomials are an important tool to approximate functions. Orthogonal rational functions provide a powerful alternative if the function of interest is not well approximated by polynomials. Polynomials orthogonal with respect to certain discrete inner products can be constructed by applying the Lanczos or Arnoldi iteration to appropriately chosen diagonal matrix and vector. This can be viewed as a matrix version of the Stieltjes procedure. The generated nested orthonormal basis can be interpreted as a sequence of orthogonal polynomials. The corresponding Hessenberg matrix, containing the recurrence coefficients, also represents the sequence of orthogonal polynomials. Alternatively, this Hessenberg matrix can be generated by an updating procedure. The goal of this procedure is to enforce Hessenberg structure onto a matrix which shares its eigenvalues with the given diagonal matrix and the first entries of its eigenvectors must correspond to the elements of the given vector. Plane rotations are used to introduce the elements of the given vector one by one and to enforce Hessenberg structure. The updating procedure is stable thanks to the use of unitary similarity transformations. In this talk rational generalizations of the Lanczos and Arnoldi iterations are discussed. These iterations generate nested orthonormal bases which can be interpreted as a sequence of orthogonal rational functions with prescribed poles. A matrix pencil of Hessenberg structure underlies these iterations. We show that this Hessenberg pencil can also be used to represent the orthogonal rational function sequence and we propose an updating procedure for this case. The proposed procedure applies unitary similarity transformations and its numerical stability is illustrated. -- Indico :: Email Notifier https://events.dm.unipi.it/e/86

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[Indico] Construction of a sequence of orthogonal rational functions,
by leonardo.robol＠unipi.it 05 Apr '22

05 Apr '22

Title: Construction of a sequence of orthogonal rational functions, Speaker(s): Raf Vandebril, Department of Computer Science, KU Leuven, Date and time: 13 Apr 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/86 Abstract -------- Orthogonal polynomials are an important tool to approximate functions. Orthogonal rational functions provide a powerful alternative if the function of interest is not well approximated by polynomials. Polynomials orthogonal with respect to certain discrete inner products can be constructed by applying the Lanczos or Arnoldi iteration to appropriately chosen diagonal matrix and vector. This can be viewed as a matrix version of the Stieltjes procedure. The generated nested orthonormal basis can be interpreted as a sequence of orthogonal polynomials. The corresponding Hessenberg matrix, containing the recurrence coefficients, also represents the sequence of orthogonal polynomials. Alternatively, this Hessenberg matrix can be generated by an updating procedure. The goal of this procedure is to enforce Hessenberg structure onto a matrix which shares its eigenvalues with the given diagonal matrix and the first entries of its eigenvectors must correspond to the elements of the given vector. Plane rotations are used to introduce the elements of the given vector one by one and to enforce Hessenberg structure. The updating procedure is stable thanks to the use of unitary similarity transformations. In this talk rational generalizations of the Lanczos and Arnoldi iterations are discussed. These iterations generate nested orthonormal bases which can be interpreted as a sequence of orthogonal rational functions with prescribed poles. A matrix pencil of Hessenberg structure underlies these iterations. We show that this Hessenberg pencil can also be used to represent the orthogonal rational function sequence and we propose an updating procedure for this case. The proposed procedure applies unitary similarity transformations and its numerical stability is illustrated. -- Indico :: Email Notifier https://events.dm.unipi.it/e/86

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Fwd: [Dipartimento.di] Seminar in Computational Mathematics - B.
by Federico Poloni 18 Mar '22

18 Mar '22

-------- Forwarded Message -------- Subject: [Dipartimento.di] Seminar in Computational Mathematics - B. Filipecki Date: Fri, 18 Mar 2022 13:40:32 +0100 From: Federico Poloni <federico.poloni(a)unipi.it> To: dipartimento(a)di.unipi.it Dear all, within the activities of the Computational Mathematics Lab, we are pleased to announce the following seminar. Title: Hierarchical Optimization of the Electrical Power Grid Speaker: Bartosz Filipecki, Department of Computer Science, University of Pisa Date/Time: Wednesday, 23 March 2022 17:00 Place: Aula Seminari Est, Dipartimento di Informatica Abstract: European electrical power networks operation is becoming more and more difficult due to increasing load and uncertainty associated with renewable energy sources. To address this problem, we consider a hierarchical approach to optimization of power grid operation. First, microgrid demand is aggregated to provide flexibility to the distribution system operator (DSO). At this stage, the optimal power flow problem (OPF) is solved in order to determine the flexibilities that can be made available to the transmission system operator (TSO). Afterwards, OPF is solved to determine the operation of the highest voltage grids, including additional constraints related to security and stability. The former provide protection against line failure, so that no blackout occurs. The latter make sure that the system does not deviate in the dynamic sense from the solution to the static OPF problem. The TSO level can also include Flexible Alternating-Current Transmission Systems Devices (FACTS). These provide us with advanced methods to control the power flow, but at a significant computational cost. After obtaining the solution, we propagate it back through the DSO level to the microgrids, which completes the framework. Everyone is welcome to attend, in person or on MS Teams: https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZGE3ZDcyOTItOTViMS00… Mauro Passacantando Federico Poloni -- --Federico Poloni Dipartimento di Informatica, Università di Pisa https://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143 ______________________________________________ Dipartimento.di mailing list Dipartimento.di(a)listgateway.unipi.it http://listgateway.unipi.it/mailman/listinfo/dipartimento.di

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[Indico] [Event reminder] Grassmann extrapolation for
by leonardo.robol＠unipi.it 17 Mar '22

17 Mar '22

Please note that the event "Grassmann extrapolation for Born-Oppenheimer Molecular Dynamics" will start on 18 Mar 2022, 11:00 (Europe/Rome). It will take place at Dipartimento di Matematica (Aula Magna). You can access the full event here: https://indico.cs.dm.unipi.it/e/76 Description ----------- Born-Oppenheimer Molecular Dynamics (BOMD) is a powerful, yet very demanding technique in computational quantum chemistry. Performing a BOMD simulation require, for each time step, to compute the energy and forces for a quantum mechanical system, which can also be embedded in a classical environment. When Density Functional Theory is used as a quantum mechanical model, the most time-consuming step for each energy/forces evaluation is the solution to the non-linear eigenvalue problem that stems from the discretization of the Kohn-Sham equations. Limiting the number of iterations required to achieve a satisfactory convergence of the procedure is therefore paramount to reduce the cost - and therefore extend the applicability - of such simulations. The most important factor in reducing the number of iteration is starting from a good guess, usually in the form of a one-body reduced density matrix. In a BOMD simulation it is possible to extrapolate information from previous steps into a new guess, however, this is not straightforward due to the nonlinear constraints that the density matrix must satisfy. In this contribution, we address this issue by performing the extrapolation on the tangent plane to the Grassmann manifold where the density is defined, by mapping the manifold to its tangent plane with a locally bijective map, which allows us to perform a linear extrapolation and then map the result back to the manifold, ensuring thus that all the physical properties of the density matrix are correctly enforced. Preliminary benchmark calculations show that the strategy is general and robust, and that even when using a naive linear extrapolation we obtain a strategy that outperforms the current state-of-the-art methods. Streaming link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 -- Indico :: Email Notifier https://indico.cs.dm.unipi.it/e/76

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[Indico] [Event reminder] Grassmann extrapolation for
by leonardo.robol＠unipi.it 08 Mar '22

08 Mar '22

Please note that the event "Grassmann extrapolation for Born-Oppenheimer Molecular Dynamics" will start on 18 Mar 2022, 11:00 (Europe/Rome). It will take place at Dipartimento di Matematica (Aula Magna). You can access the full event here: https://indico.cs.dm.unipi.it/e/76 Description ----------- Born-Oppenheimer Molecular Dynamics (BOMD) is a powerful, yet very demanding technique in computational quantum chemistry. Performing a BOMD simulation require, for each time step, to compute the energy and forces for a quantum mechanical system, which can also be embedded in a classical environment. When Density Functional Theory is used as a quantum mechanical model, the most time-consuming step for each energy/forces evaluation is the solution to the non-linear eigenvalue problem that stems from the discretization of the Kohn-Sham equations. Limiting the number of iterations required to achieve a satisfactory convergence of the procedure is therefore paramount to reduce the cost - and therefore extend the applicability - of such simulations. The most important factor in reducing the number of iteration is starting from a good guess, usually in the form of a one-body reduced density matrix. In a BOMD simulation it is possible to extrapolate information from previous steps into a new guess, however, this is not straightforward due to the nonlinear constraints that the density matrix must satisfy. In this contribution, we address this issue by performing the extrapolation on the tangent plane to the Grassmann manifold where the density is defined, by mapping the manifold to its tangent plane with a locally bijective map, which allows us to perform a linear extrapolation and then map the result back to the manifold, ensuring thus that all the physical properties of the density matrix are correctly enforced. Preliminary benchmark calculations show that the strategy is general and robust, and that even when using a naive linear extrapolation we obtain a strategy that outperforms the current state-of-the-art methods. Streaming link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 -- Indico :: Email Notifier https://indico.cs.dm.unipi.it/e/76

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Annunci di seminari NumPI
by Leonardo Robol 08 Mar '22

08 Mar '22

Cari tutti, d'ora in poi -ammesso che la cosa funzioni bene- useremo la piattaforma Indico per inviare gli annunci dei seminari sulla mailing list, dato che lo fa in automatico (reminder inclusi, cosa che io tendo a dimenticare piuttosto facilmente). A breve dovrebbe arrivarne uno. Il formato dell'annuncio sarà leggermente diverso rispetto al solito, ma si tratta sempre dei seminari NumPi. A presto, -- Leonardo.

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Seminar announcement
by Fabio Durastante 07 Mar '22

07 Mar '22

Speaker: Nicola Guglielmi Affiliation: Gran Sasso Science Institute Venue: Aula Volterra, Scuola Normale Superiore *Remark. *Il seminario si terrà in presenza. Chi fosse interessato a partecipare deve scrivere a classi(a)sns.it _entro le 9:00 di Lunedì __ __7 marzo 2022_ *Abstract. *Stability and robustness analysis of linear continuous and discrete dynamical systems is a vast and active interdisciplinary research area. Although the word stability is used in many different contexts, in this talk it is meant to indicate the broad spectrum of issues that arise in the analytical and numerical study of dynamical and control systems, especially in relation to qualitative information of the system under study. These issues result from the need to develop stable and reliable systems robustly preserving essential qualitative properties. The analysis of these features is often based on eigenvalue optimization or on pseudospectral measures of a certain matrix A, where the structure of A (e.g., sparse, Hamiltonian, nonnegative, Toeplitz, etc.) plays an important role. The main goal of this talk is to show how these structured distances can be approximated. The proposed method is a two-level iterative algorithm, where in an inner iteration a gradient flow drives perturbations to the original matrix of a fixed size into a minimum of a functional that depends on eigenvalues (and possibly eigenvectors), and in an outer iteration the perturbation size is optimized such that the functional reaches some target value (for example O). An interesting point - related to certain low-rank properties of extremizers - lies in the possibility of considering gradient flows on low-rank manifolds. The talk is mainly inspired by joint works with Christian Lubich (Tuebingen). Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Seminar announcement
by Fabio Durastante 23 Feb '22

23 Feb '22

Speaker: Leonardo Robol Affiliation: Università di Pisa Venue: Aula Magna, Dipartimento di Matematica Time: Thursday, 24/02/2022, 11:00 Title: Sampling the eigenvalues of random matrices Random matrices (that is, matrices with random variables as entries) appear in several areas of mathematics and physics. Often, one is interested in sampling their eigenvalues (which are again random variables); we briefly recap the main tools that can be used to sample the joint eigenvalue distribution for Hermitian matrices from the Gaussian unitary Ensemble (GUE) with O(n^2) flops, and discuss how similar ideas can be used to efficiently perform the analogous operation for Haar-distributed orthogonal or unitary matrices. The latter operation requires to find a suitable compact canonical form for upper Hessenberg unitary matrices obtained by reducing random orthogonal/unitary matrices, and then efficiently operate on this compact representation to compute the eigenvalues. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Annuncio di seminario 10/02
by Fabio Durastante 10 Feb '22

10 Feb '22

Speaker: Milo Viviani Affiliation: Scuola Normale Superiore Venue: Aula Magna, Dipartimento di Matematica Time: Thursday, 10/02/2022, 11:00 Title:Solving cubic matrix equations arising in conservative dynamics Spatial semi-discretization of conservative PDEs can be described as flows in suitable matrix spaces, which in turn leads to the need to solve polynomial matrix equations, a classical and important topic both in theoretical and in applied mathematics. Solving these equations numerically is challenging due to the presence of several conservation laws which our finite models incorporate and which must be retained while integrating the equations of motion. In the last thirty years, the theory of geometric integration has provided a variety of techniques to tackle this problem. These numerical methods require to solve both direct and inverse problems in matrix spaces. We present two algorithms to solve a cubic matrix equation arising in the geometric integration of isospectral flows. This type of ODEs includes finite models of ideal hydrodynamics, plasma dynamics, and spin particles, which we use as test problems for our algorithms. Meeting link:https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Corso di dottorato: Low-rank approximation techniques for matrices
by Leonardo Robol 14 Jan '22

14 Jan '22

Buongiorno, segnalo il corso di dottorato "Low rank approximation techniques for matrices and tensors", che sarà tenuto a partire del prossimo 7 febbraio da Stefano Massei presso il dipartimento di Informatica. È un corso concentrato in 3 settimane; in quel periodo Stefano sarà ospite del Dipartimento di Matematica. Riporto qui sotto ulteriori informazioni, che in ogni caso trovate sulla pagina web del corso di dottorato in Computer Science [1]. ===================================================================== Low rank approximation techniques for matrices and tensors Lecturers: Stefano Massei (TU/e, The Netherlands) Period: From February 7th to February 26th, 2022 Schedule: 6 hours the first and second week, 4 hours the third week To attend the course send an email to s.massei(a)tue.nl Matrices and tensors are the heart of many scientific and industrial computational problems. In this course we will survey numerical methods that leverage low-rank structures in matrices and tensors in order to reduce the consumption of computational resources while maintaining a satisfactory accuracy. The course will touch the following topics: * Low-rank tensor formats: Tucker and tensor train * Deterministic and randomized algorithms for low-rank approximation of matrices and tensors * Trace and diagonal estimation of black box matrices [1] https://dottorato.di.unipi.it/phd-programme/teaching/phd-courses-a-y-2021-2…

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Spostamento mailing list
by Leonardo Robol 09 Dec '21

09 Dec '21

Cari tutti, stiamo provando a spostare la mailing list NumPi su un nuovo server, per permettere anche ai non-unipi di iscriversi in autonomia. Per ora è un tentativo sperimentale, ma se leggete questo messaggio è già un buon segno; l'indirizzo a cui scrivere cambia, e diventa numpi(a)lists.dm.unipi.it. Se vediamo che tutto va bene, faremo puntare il vecchio alias (numpi(a)di.unipi.it) a questo nuovo indirizzo, in modo che il passaggio sia il più indolore possibile. Le vecchie iscrizioni e preferenze sono state importate; segnalatemi pure ogni problema che doveste notare! A presto, -- Leonardo Robol.

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Annuncio di seminario, 6/12 (Bruno Iannazzo)
by Leonardo Robol 02 Dec '21

02 Dec '21

Speaker: Bruno Iannazzo Affiliation: Università degli studi di Perugia Venue: Aula Magna, Dipartimento di Matematica Time: Lunedì, 6/12/2021, 15:00 Title: New geometries on positive-definite matrices and their relation to the power means We introduce a new family of geometries on the cone of positive definite matrices obtained from the Hessian of the power potential and provide explicit expressions for related quantities such as geodesics and distances. This generalizes in some sense the geometry obtained from the Hessian of the logarithmic potential, whose geodesic has been understood as the weighted geometric mean of two matrices. Indeed, the new geometries provide a definition of matrix power mean alternative to the existing ones. We discuss some properties of the proposed power mean and relate it with the geometric mean. Finally, we discuss on how these geometries can be used to accelerate the convergence of optimization algorithms for the matrix geometric mean of several variables. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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[NOMADS] Seminar - Matthew Colbrook - Dec 1 at 17:00
by Francesco Tudisco 29 Nov '21

29 Nov '21

Dear all, We are starting this week a new series of NOMADS seminars on Numerical methods, Matrix analysis and Data Science. This week's seminar will take place on *Wednesday December 1 at 17:00* (CET) in the *GSSI Main Lecture Hall* (the "red" conference hall by the entrance of the lecture rooms building). The speaker is Matthew J Colbrook from University of Cambridge and ENS Paris, with a talk on the computation of semigroups of fractional PDEs. Title and abstract are below. In person participation is encouraged, but remote attendance will also be possible via the link: https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09 Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Hope to see you all on Wednesday! And, please feel free to distribute this announcement as you see fit. Francesco and Nicola ----------- Title: Computing semigroups and time-fractional PDEs with error control Abstract: We develop an algorithm that computes strongly continuous semigroups on infinite-dimensional Hilbert spaces with explicit error control. Given a generator $A$, a time $t > 0$, an arbitrary initial vector $u_0$ and an error tolerance $\epsilon > 0$, the algorithm computes $\exp(tA)u_0$ with error bounded by $\epsilon$. The (parallelisable) algorithm is based on a combination of a regularized functional calculus, suitable contour quadrature rules and the adaptive computation of resolvents in infinite dimensions. As a particular case, we deal with semigroups on $L^2(R^d)$ that are generated by partial differential operators with polynomially bounded coefficients of locally bounded total variation. For analytic semigroups, we provide a quadrature rule whose error decreases like $\exp(−cN/ log(N))$ for $N$ quadrature points, that remains stable as $N \to \infty$, and which is also suitable for infinite-dimensional operators. Finally, we extend the method to time-fractional PDEs (where it avoids singularities as $t \to 0$ and large memory consumption). Numerical examples are given, including: Schrödinger and wave equations on the aperiodic Ammann–Beenker tiling and fractional beam equations arising in the modelling of small-amplitude vibration of viscoelastic materials. The spectral analysis (which is always needed for contour methods) is considerably simplified due to an infinite-dimensional “solve-then-discretise” approach. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/CAO2_FWmWATOjsjz5v5…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Annuncio di seminario, 19/11 (Mariarosa Mazza)
by Leonardo Robol 18 Nov '21

18 Nov '21

Speaker: Mariarosa Mazza Affiliation: Università dell'Insubria Venue: Aula Magna, Dipartimento di Matematica Time: Venerdì, 19/11/2021, 10:00 Title: Caputo and Riemann-Liouville fractional derivatives: a matrix comparison Fractional derivatives are a mathematical tool that received much attention in the last decades because of their non-local behavior which has been demonstrated to be useful when modeling anomalous diffusion phenomena appearing, e.g., in imaging or electrophysiology. Two of the most famous definitions of fractional derivatives are the Riemann- Liouville and the Caputo ones. The two formulations are related by a well-known formula that expresses a Riemann-Liouville derivative as a Caputo one plus a term that depends on the function and its derivatives at the boundary. As a consequence of this relation, Riemann-Liouville and Caputo derivatives coincide only for sufficiently smooth functions that satisfy homogeneous conditions at the boundary. Aiming at uncovering how much this discrepancy reflects on their discretized counterparts, we focus on the relation between Riemann-Liouville and Caputo derivatives once approximated by a collocation method based on B-splines, i.e., high order finite elements with maximum regularity. We show that when the fractional order α ranges in (1,2) their difference in terms of matrices corresponds to a rank-1 correction whose spectral norm increases with the mesh-size n and is o(√n). On one hand, this implies that the spectral distribution for the B-spline collocation matrices corresponding to the Riemann-Liouville and Caputo derivatives coincide; on the other hand, the presence of the rank-1 correction makes the Caputo matrices worse conditioned for α tending to 1 due to a larger maximum singular value. Some linear algebra consequences of all this knowledge are discussed, and a selection of numerical experiments that validate our findings is provided together with a numerical study of the approximation behavior of B-spline collocation. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Annuncio di seminario, 25/10 (Cecilia Pagliantini)
by Leonardo Robol 25 Oct '21

25 Oct '21

Speaker: Cecilia Pagliantini Affiliation: TU Eindhoven Venue: Sala Seminari, Dipartimento di Matematica Time: Monday, 25/10/2021, 15:00 Title: Structure-preserving dynamical model order reduction of parametric Hamiltonian systems In real-time and many-query simulations of parametric differential equations, computational methods need to face high computational costs to provide sufficiently accurate and stable numerical solutions. To address this issue, model order reduction techniques aim at constructing low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. In this talk, we will consider reduced basis methods (RBM) for the model order reduction of parametric Hamiltonian dynamical systems describing nondissipative phenomena. The development of RBM for Hamiltonian systems is challenged by two main factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics, such as invariants of motion or symmetries, might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the \emph{local} low-rank nature of transport-dominated and nondissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations. We will discuss how to address these aspects via a structure-preserving nonlinear reduced basis approach based on dynamical low-rank approximation. The gist of the proposed method is to evolve low-dimensional surrogate models on a phase space that adapts in time while being endowed with the geometric structure of the full model. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Annuncio di seminario, 15/10 (Igor Simunec)
by Leonardo Robol 15 Oct '21

15 Oct '21

Cari tutti, a breve ricominceremo con i tradizionali seminari NumPi, questa volta in forma "ibrida". Per tutti quelli che vorranno ci sarà la possibilità di seguire in presenza in Aula Magna del Dipartimento di Matematica (compilando questa form: https://forms.gle/AaMgajhKhroXdHqY6). Per gli altri, organizzeremo lo streaming tramite il solito link ( https://hausdorff.dm.unipi.it/b/leo-xik-xu4). Qui sotto trovate l'annuncio del primo seminario; a breve vi farò avere un Doodle per provare a scegliere un giorno che torni il più comodo possibile a tutti, da utilizzare per quelli successivi. Trovate tutte le informazioni sulla pagina dei seminari del sito NumPi (https://numpi.dm.unipi.it/seminars). A presto, -- Leonardo. Speaker: Igor Simunec Affiliation: Scuola Normale Superiore, Pisa Time: Friday, 15/10/2021, 16:30 Title: Computation of generalized matrix functions with rational Krylov methods Generalized matrix functions [3] are an extension of the notion of standard matrix functions to rectangular matrices, defined using the singular value decomposition instead of an eigenvalue decomposition. In this talk, we consider the computation of the action of a generalized matrix function on a vector and we present a class of algorithms based on rational Krylov methods [2]. These algorithms incorporate as a special case previous methods based on the Golub-Kahan bidiagonalization [1]. By exploiting the quasiseparable structure of the projected matrices, we show that the basis vectors can be updated using a short recurrence, which can be seen as a generalization to the rational case of the Golub-Kahan bidiagonalization. We also prove error bounds that relate the error of these methods to uniform rational approximation on an interval containing the singular values of the matrix. The effectiveness of the algorithms and the accuracy of the bounds is illustrated with numerical experiments. This is joint work with Angelo A. Casulli (Scuola Normale Superiore). [1] F. Arrigo, M. Benzi, and C. Fenu, Computation of generalized matrix functions, SIAM J. Matrix Anal. Appl. 37 (2016), no. 3, 836–860. [2] A. A. Casulli, I. Simunec, Computation of generalized matrix functions with rational Krylov methods, arXiv:2107.12074 (2021). [3] J. B. Hawkins and A. Ben-Israel, On generalized matrix functions, Linear and Multilinear Algebra 1 (1973), no. 2, 163–171. Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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Orario per seminari NumPi
by Leonardo Robol 13 Oct '21

13 Oct '21

Cari tutti, a partire dal prossimo seminario (dopo quello di Igor venerdì) cercheremo di scegliere un orario compatibile con gli impegni di tutti, e mantere una cadenza indicativamente bisettimanale. Ho creato un Doodle [1] per la settimana 25/10 - 29/10, dove chiederei (a chi è interessato a seguire i seminari in presenza e/o online) di indicare le preferenze di orario. Sebbene il Doodle sia per quella settimana specifica, è da intendersi come le preferenze in base ai vostri impegni settimanali. Vi chiederei di farci avere una risposta entro venerdì, così che possiamo organizzare il seminario seguente basandoci sulle risposte. Grazie! A presto, -- Leonardo (e Fabio). [1] https://doodle.com/poll/dtvyu6uakv3exdp8

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PhD position in Prague
by Leonardo Robol 12 Aug '21

12 Aug '21

Cari tutti, inoltro un messaggio da Stefano Pozza, su una borsa di dottorato disponibile alla Charles University, Praga. Trovate i dettagli in fondo alla mail. Buone vacanze, -- Leonardo. ----------------------------------------------------------------------- Ph.D. Position, Dep Num Math, Charles Univ, Czech Rep A Ph.D. position is available within the framework of the Primus Research Programme: "A Lanczos-like Method for the Time-Ordered Exponential" at the Faculty of Mathematics and Physics, Charles University, Prague. The four years of Ph.D. studies will take place in the Department of Numerical Mathematics under the supervision of Dr. Stefano Pozza (PI of the project). The department offers an international environment at one of the top universities in the Czech Republic, and the oldest university in Central Europe. The student will also have the opportunity to work with external collaborators from France, Italy, and the UK. The applicants must hold a Master's degree by the start date of Spring 2022 (to be announced) and have a strong interest in numerical linear algebra and numerical analysis. Knowledge of Matlab or other programming languages is necessary. Applicants will have to prove their English language level by passing an exam (it is possible to waive the examination under some conditions). Application deadline: September 30, 2021. More information and application instructions: https://www.starlanczos.cz/open-positions

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Cena NumPi
by Leonardo Robol 30 Jun '21

30 Jun '21

Cari tutti, come gli anni scorsi (ed in particolare quelli non-pandemici), vorremmo provare ad organizzare una cena di "fine seminari"; più che altro sarebbe una scusa per vedersi, a maggior ragione quest'anno dove non ci siamo (quasi) mai incontrati di persona. Ho predisposto un Doodle dove potete segnare la vostra disponibilità, se intendete partecipare: https://doodle.com/poll/z2xw2k6u5zzfybn3 Siete tutti benvenuti (dagli ordinari ai dottorandi, ma anche simpatizzanti, ecc.). Vi chiederei solo di segnare la vostra presenza quanto prima così che riusciamo ad organizzarci per bene. Il luogo non è stato ancora scelto, ma proposte sono sempre bene accette; probabilmente dovremo scegliere anche in funzione del numero di partecipanti. A presto! -- Leonardo Robol.

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